Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#19151414 | C2 | semidirect |
| 5. #26021040 | C2 | semidirect |
| 6. #26018339 | C2 | semidirect |
| 7. C2×#362×C89 | C2 | semidirect |
| 172. C2×#362 | D89 | semidirect |
| 176. C89 | #13418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030741 | 2 |
| #26021999 | 2 |
| C2×#19151414 | 2 |
| #26021981 | 2 |
| #26021040 | 2 |
| #26018339 | 2 |
| C2×#362×C89 | 2 |
| #13418 | 89 |